In a certain country, 7% of the population have a certain disease. A diagnostic
ID: 2976967 • Letter: I
Question
In a certain country, 7% of the population have a certain disease. A diagnostic blood test has been developed for the disease. If a person has the disease, the result is positive 93% of the time while if he doesn't has the disease, the result is positive 1% of the time. If a person gets a positive blood test, what is the probability that he has the disease? The same test is used in another country, and it is found that 13% of a sample population tests positive. If we assume this sample is representative, what fraction of the population has the disease?Explanation / Answer
A = event with person having disease and tests positive
B = event with person not having disease but tests positive
P(A)= 0.07*0.93=0.0651
P(B)=0.93*0.01=0.0093
If a person gets a positive blood test, the probability that he has the disease = P(A)/P(A)+P(B) = 0.0651/0.0651+0.0093 = 0.875
Let x% of people have disease
P(A) = (x/100)*0.93
P(B) = ((100-x)/100)*0.01
Given P(A)+P(B) = 0.13
so
0.93x + 1 -0.01x = 13
0.92x = 12
x = 13.0431%
Fraction of the population has the disease = 12/0.92